Given, a random sample from $N(0,1)$. Investigate the behavior of $T =(X_1 + X_2)/3$ in terms of unbiasedness, consistency, efficiency and sufficiency.
What I don't understand is, there is no unknown parameter here. Then what is the estimator for?
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Sign up to join this communityGiven, a random sample from $N(0,1)$. Investigate the behavior of $T =(X_1 + X_2)/3$ in terms of unbiasedness, consistency, efficiency and sufficiency.
What I don't understand is, there is no unknown parameter here. Then what is the estimator for?
This is the usual situation when using simulation to investigate properties of estimators. You have designed the simulation, so you know the values of the "unknown" parameters. Still this might be a useful exercise!
As said in a comment by user whuber:
The properties of a statistical estimator do not depend on the state of mind of its user. Whether or not you happen to know the parameter, you can still investigate how well the estimator works to identify that parameter.